Make note of the colors of the 3 wires on the connector. (It's a 3-pin Molex SPOX female connector, with a 3.96 mm pitch.)

Cut the wires close to the connector.

Install a replacement connector. I used a Molex connector from a PC power supply cable in my junk collection. Cut down the connector to 3 wires.

You could also adapt a PC fan extension cable. Like this VCOM 12-Inch VC-POW3EXT 3-PIn to 3-Pin Fan Extension Cable (CE311-12INCH)

Solder the wires and use heat-shrink tubing for a secure connection.